KSEEB SSLC Solutions for Class 10 Maths – Statistics (English Medium)
Exercise 6.1:
Question 1:
Calculate the standard deviation of the following data.
x | 3 | 8 | 13 | 18 | 23 |
f | 7 | 10 | 15 | 10 | 8 |
Solution :
x | f | fx | x^{2} | fx^{2} |
3 | 7 | 21 | 9 | 63 |
8 | 10 | 80 | 64 | 640 |
13 | 15 | 195 | 169 | 2535 |
18 | 10 | 180 | 324 | 3240 |
23 | 8 | 184 | 529 | 4232 |
n = 50 | ∑fx = 660 | ∑fx^{2} = 10710 |
Question 2:
The number of books bought by 200 students in a book exhibition is given below.
No. of books | 0 | 1 | 2 | 3 | 4 |
No. of students | 35 | 64 | 68 | 18 | 15 |
Find the variance and standard variation.
Solution :
No. of Books (x) |
No. of
students (f) |
Fx | d^{2} | fd^{2} | |
0 | 35 | 0 | -1.57 | 2.465 | 86.275 |
1 | 64 | 64 | -0.57 | 0.325 | 20.8 |
2 | 68 | 136 | 0.43 | 0.185 | 12.58 |
3 | 18 | 54 | 1.43 | 2.045 | 36.81 |
4 | 15 | 60 | 2.43 | 5.905 | 88.575 |
n = 200 | ∑fx = 314 | ∑fd^{2} = 245.04 |
Question 3:
The daily minimum temperature recorded (in degrees F) at a place on a hill station during a week was as follows:
Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
4.1 | 3.2 | 2.1 | 1.8 | 1.6 | 2.2 | 1.4 |
Calculate the variance and standard deviation. Interpret the results.
Online standard deviation calculator, calculation selected standard deviation, RMS. How to calculate the standard deviation?
Solution :
Question 4:
The marks scored by 60 students in a science test are given below.
Marks (x) | 10 | 20 | 30 | 40 | 50 | 60 |
No. of students (f) | 8 | 12 | 20 | 10 | 7 | 3 |
Calculate the variance and standard deviation.
Solution :
Question 5:
The daily wages of 40 workers of a factory are given in the following table.
Wages in Rs. | 30-34 | 34-38 | 38-42 | 42-46 | 46-50 | 50-54 |
No. of workers | 4 | 7 | 9 | 11 | 6 | 3 |
Calculate (i) Mean (ii) Variance and (iii) Standard deviation of wages and interpret the findings.
Solution :
C.I | f | x | fx | d^{2} | fd^{2} | |
30-34 | 4 | 32 | 128 | -9.7 | 94.09 | 376.36 |
34-38 | 7 | 36 | 252 | -5.7 | 32.49 | 227.43 |
38-42 | 9 | 40 | 360 | -1.7 | 2.89 | 26.01 |
42-46 | 11 | 44 | 484 | 2.3 | 5.29 | 58.19 |
46-50 | 6 | 48 | 288 | 6.3 | 39.69 | 238.14 |
50-54 | 3 | 52 | 156 | 10.3 | 106.09 | 318.27 |
n = 40 | ∑fx = 1668 | ∑fd^{2 }= 1244.4 |
Question 6:
Calculate (i) Arithmetic mean and (ii) Standard deviation for the following frequency distribution.
C.I | 20-25 | 25-30 | 30-35 | 35-40 | 40-45 | 45-50 |
f | 8 | 3 | 15 | 12 | 8 | 4 |
Solution :
c
Question 7:
Find the variance and standard deviation for the following distribution.
C.I | 3.5-4.5 | 4.5-5.5 | 5.5-6.5 | 6.5-7.5 | 7.5-8.5 |
f | 9 | 14 | 22 | 11 | 17 |
Solution :
Question 8:
Mean of 100 items is 48 and their standard deviation is 10. Find the sum of all the items and the sum of the squares of all the items.
Solution :
Question 9:
In a study of diabetic patients in a village, the following observations were noted:
Age in years | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |
No. of patients | 2 | 5 | 12 | 19 | 9 | 4 |
Calculate the mean and standard deviation. Also interpret the results.
Solution :
Question 10:
A group of 45 house owners contributed money towards the development of green environment in a locality. The amount of money collected per month is shown below.
Amount (Rs.) | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 |
No. of house owners |
2 | 7 | 12 | 19 | 5 |
Calculate the variance and standard deviation.
Solution :
Exercise 6.2:
Question 1:
Calculate the coefficient of variation of the following data: 40, 36, 64, 48, 52.
Solution :
Question 2:
The scores of a batsman in 8 innings are given as: 48, 40, 36, 35, 46, 42, 36, 37. Calculate
(i) Mean (ii) Standard deviation
(iii) Coefficient of variation.
Solution :
Question 3:
If the coefficient of variation of a collection of data is 45 and its standard deviation is 2.5, then find the mean.
Solution :
Question 4:
A group of 100 candidates attending a physical test for recruitment have their average height as 163.8 cm with coefficient of variation 3.2. What is the standard
deviation of their heights?
Solution :
Question 5:
The coefficient of variations of two series are 58 and 69. Their standard deviations are 21.2 and 51.6. What are their arithmetic means?
Solution :
Question 6:
Batsman A gets an average of 64 runs per innings with standard deviation of 18 runs, while batsman B gets an average score of 43 runs with standard deviation of 9 runs in an equal number of innings. Discuss the efficiency and consistency of both the batsmen.
Solution :
Question 7:
Solution :
Question 8:
In two construction companies A and B, the average weekly wages in rupees and the standard deviations are as follows:
Determine which factory has greater variability in individual wages?
Company | Average of wages
(in Rs.) |
S.D. of wages (in Rs.) |
A B |
3450
2850 |
6.21 4.56 |
Solution :
Question 9:
Calculate
(i) Arithmetic mean
(ii) Standard deviation and
(iii) coefficient of variation for the following frequency distribution.
Class interval | Frequency |
30-35 35-40 40-45 45-50 50-55 |
5 10 16 15 4 |
Solution :
Question 10:
Marks obtained in the test by students of two sections A and B are given below.
Marks | No. of students | No. of students |
25-30 30-35 35-40 40-45 45-50 |
5
10 25 8 2 |
5 12 20 8 5 |
Determine:
(i) Which section’s performance is better?
(ii) Which section’s performance is more variable?
Solution :
Exercise 6.3:
Question I(1):
Draw a pie chart to represent the following data.
The number of students who are willing to join their favourite sports.
Name of the sport | Foot ball | Tennis | Volley ball | Hockey | Basket ball | Other |
Number of students | 35 | 14 | 10 | 6 | 5 | 2 |
Solution :
Question I(2):
Draw a pie chart to represent the following data.
The survey carried out in the class regarding places of visit for excursion and the number of students who opted each place.
Places | Mysore | Bijapur | Gokarna | Chitradurga |
Number of students | 14 | 6 | 2 | 18 |
Solution :
Question I(3):
Draw a pie chart to represent the following data.
The number of books issued to students by a school library on each day of the week.
Day | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
Number of books issued | 52 | 124 | 168 | 84 | 36 | 16 |
Solution :
Question I(4):
Draw a pie chart to represent the following data.
The ages of the drivers of cars involved in fatal accidents during a certain year.
Age of driver (in years) | under 25 | 25 to 40 | 40 to 60 | Above 60 |
% of drivers | 15% | 60% | 20% | 5% |
Solution :
Question I(5):
Draw a pie chart to represent the following data.
A survey was conducted to study the various brands of soaps used by people in a village.
Brand of soap | A | B | C | Other |
Percent of Villagers | 50% | 30% | 15% | 5% |
Solution :
Question II(1):
Study the pie chart given below and answer the questions.
The given pie chart shows the annual agricultural yield of a certain place. If the total production is 8100 tons,
Answer the following questions
- What is the yield in tons of rice, ragi, sugar cane and others.
- How much percent do the production of ragi exceeds that of rice?
- If the yield of sugarcane on a different year was 2400 tons, find the yield of rice.
Solution :
Question II(2):
Study the pie chart given below and answer the questions.
A group of people were interviewed and asked which T.V. channel they liked the most. The results are shown in the pie chart.
Answer the questions.
i. What fraction of the people who were interviewed watched
(a) Channel 3
(b) Channel 5
(c) Channel 1
(d) Channel 2
(e) Channel 9
ii. If there were 200 people, how many viewed each of the Channels.
Solution :
Question II(3):
Study the pie chart given below and answer the questions.
A housewife was asked to estimate how she spent time on a particular day from 5.00 a.m. to 8.00 pm. The results are shown on the pie chart given below
i. What fraction of the time did she spend on each of the activities?
ii. What percentage of time did she spend on
(a) washing
(b) cleaning
(c) cooking.
Solution :
i. Measure of each item:
Cleaning = 120°
Washing = 60°
Lunch and tea breaks = 48°
Shopping = 60°
Cooking = 72°
Question II(4):
Study the pie chart given below and answer the questions.
i. What percent of the total weight of human body is equivalent to the weight of the proteins in skin in human body?
ii. What will be the quantity of water in the body of a person weighing 50 kg?
iii. What is the ratio of distribution of proteins in the muscles to that of the distribution of proteins in the bones?
iv. In the human body, what part is made of bones or skin?
v. What should be the central angle to represent the distribution of proteins and other dry elements in the human body?
Solution :
Question II(5):
The pie chart given below shows the percentage distribution of the expenditure incurred in publishing a book. Study the pie chart and answer the questions.
i. If the total expenditure incurred is Rs. 3,60,000 what is the expenditure incurred for each of the items?
ii. If for a certain quantity of books, the publisher has to pay Rs. 30,600 as printing cost, then what is the amount of royalty to be paid for these books?
iii. By what percentage is the royalty on the book less than paper cost?
iv. By what percentage is the binding cost more than transport cost?
v. If the transport cost incurred is Rs. 36,600, what will be the binding cost?
vi. How much is the binding cost less than the printing cost, if the printing cost incurred is Rs. 52, 600?
vii. If 5500 copies are published and the transportation cost on them amounts to Rs. 82,500, then what should be the selling price of the book so that the publisher can earn a profit of 25%?
viii. The price of a book is marked 20% above the cost price. If the marked price of the book is Rs. 180, then what is the cost of the paper used in a single copy of the book?